Navier–Stokes Equations and Bulk Viscosity for a Polyatomic Gas with Temperature-Dependent Specific Heats

Abstract

A system of Navier–Stokes-type equations with two temperatures is derived, for a polyatomic gas with temperature-dependent specific heats (thermally perfect gas), from the ellipsoidal statistical (ES) model of the Boltzmann equation extended to such a gas. Subsequently, the system is applied to the problem of shock-wave structure for a gas with large bulk viscosity (or, equivalently, with slow relaxation of the internal modes), and the numerical results are compared with those based on the ordinary Navier–Stokes equations. It is shown that the latter equations fail to describe the double-layer structure of shock profiles for a gas with large bulk viscosity.

Keywords

• polyatomic gases
• bulk viscosity
• Navier–Stokes equations
• ES model
• shock-wave structure
• thermally perfect gases